Sampling the augmentation distribution \(\lambda ^{\star }\)  can be difficult when \(\mathcal {G}\)  is not finite and \(f_{\theta }\)  is a deep neural network. Even when the transformation space is low dimensional, as in the case of translations and rotations, the highly non-convex loss landscape of these models makes the maximization over \(\mathcal {G}\)  challenging [1]}. If the optimal distribution \(\lambda ^{\star }\)  is not smooth, it is challenging to sample from it with sufficient accuracy [2]}. Consequently, obtaining an unbiased estimator of \(\mathbb {E}_{g \sim \lambda ^{\star }}\left[ \ell (f_{\theta }(g\mathbf {x}), y) \right]\)  may not be possible. Therefore, we add an \(L_2\)  norm penalisation, which promotes smoothness, to leverage MCMC methods.
